Mathematics: Find the equation of the line which passes through the point (−3, 5) and is perpendicular to the line 4x + 3y = 6. express your answer in slope-intercept form.

Find the equation of the line which passes through

justintisdale95

11.03.2022

$y=\dfrac{3}{4}x+7\dfrac{1}{4}$

Step-by-step explanation:

$k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\ \iff\ m_1m_2=-1$

Let $k:4x+3y=6\to 3y=-4x+6\ \ \ \ |:3\\\\y=-\dfrac{4}{3}x+2\\\\m_1=-\dfrac{4}{3}$

$l:y=m_2x+b\\\\l\ \perp\ k\ \iff\ -\dfrac{4}{3}m_2=-1\qquad|\cdot\left(-\dfrac{3}{4}\right)\\\\m_2=\dfrac{3}{4}\\\\l:y=\dfrac{3}{4}x+b$

The line l passes through the point (-3, 5).

Substitute the coordinates of the point to the equation of the function l:

$5=\dfrac{3}{4}(-3)+b\\\\5=-\dfrac{9}{4}+b\\\\5=-2\dfrac{1}{4}+b\qquad|+2\dfrac{1}{4}\\\\b=7\dfrac{1}{4}$

Finally $l:y=\dfrac{3}{4}x+7\dfrac{1}{4}$

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dyanaycooper13

20.11.2022

-1

Step-by-step explanation:

I just did it on edge and its correct 100%

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